A New Lower Bound on the Density of Vertex Identifying Codes for the Infinite Hexagonal Grid

Given a graph G, an identifying code D V (G) is a vertex set such that for any two distinct vertices v1, v2 V (G), the sets N[v1] D and N[v2] D are distinct and nonempty (here N[v] denotes a vertex v and its neighbors). We study the case when G is the infinite hexagonal grid H. Cohen et.al. constructed two identifying codes for H with density 3/7 and proved that any identifying code for H must have density at least 16/39 0.410256. Both their upper and lower bounds were best known until now. Here we prove a lower bound of 12/29 0.413793.

• Type: Journal
• Year: 2010
• Where: CORR
• Authors: Daniel W. Cranston, Gexin Yu
• Keywords: Code, CORR 2010, Distinct Vertices, Education, Infinite Hexagonal Grid